A new study in the Journal of Sports Economics finds that shorter NBA refs may call more fouls, in an excellent manifestation of the Napoleon Complex. Paul Gift and Ryan Rodenberg looked at 4,463 regular season games from 2008 to 2012, and—controlling for variables like race and experience*—found a relationship between the average heights of three-man refereeing crew and the foul rate (per 48 minutes) of the players they officiated.

Splitting the officiating crews into three height groups, Gift and Rodenberg posted these results:

6' 0'' and under

6' 0'' to 6' 3''

6'3'' and over

p-value

Personal fouls/48

4.13

4.09

4.03

0.03

FT attempted/48

4.86

4.79

4.68

0.01

FT made/48

3.71

3.65

3.56

0.00

This isn't a large effect—an average player would have around one more foul every 480 minutes if the crew's average height was under 6 feet instead of over 6-foot-3—but it's statistically valid . The researchers' ANOVA analysis also looked at other stats like rebounds, field goals, and blocks, but nothing else had a significant link (p < 0.05) to the height of the ref crew.

The researchers had to reconstruct the refs' heights themselves and did not list them individually. Joey Crawford is definitely shorter than 6 feet, though.

*All of the controlled variables: Player height, age, position, starting status, and whether they're home or away; ref age, officiating experience, basketball experience, level of education, race, and "quality," as judged by an independent ranking system similar to the NBA's own internal tracking.